Unitary equivalence to a complex symmetric matrix: Low dimensions

作者：Garcia Stephan Ramon^*; Poore Daniel E; Tener James E

来源：Linear Algebra and Its Applications, 2012, 437(1): 271-284.

DOI：10.1016/j.laa.2012.01.029

• Complex symmetric matrix
• Complex symmetric operator
• Unitary equivalence
• Unitary similarity
• Unitary orbit
• Transpose
• Trace
• Nilpotent
• Truncated Toeplitz operator
• UECSM
• Words
• SU(p, q)

A matrix T is an element of M-n(C) is UECSM if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely characterize 4 x 4 nilpotent matrices which are UECSM and we settle an open problem which has lingered in the 3 x 3 case. We conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above.

• 出版日期2012-7-1